Methods and Results
I ran four regressions to estimate simple linear regressions and then
model the visualizations as closely as possible.
First regression: log of ACRES on log of HPI without
TWFE. This regression estimates the simple linear effect of a 1%
increase in CRP acres on the percentage increase of HPI.
Second regression: log of ACRES on log of HPI with
county and year TWFE. This regression estimates the simple linear effect
of a 1% increase in CRP acres on the percentage increase of HPI, after
controlling for county and year fixed effects.
Third regression: log of ACRES on log of HPI with
polynomials but without TWFE. This regression estimates the non-linear
effect of a 1% increase in CRP acres on the percentage increase of HPI.
A cubic polynomial is included to most closely match the conditional
expectation that appeared to have three distinct sloped areas.
Fourth regression: log of ACRES on log of HPI with
polynomials and with TWFE. This regression estimates the non-linear
effect of a 1% increase in CRP acres on the percentage increase of HPI.
A quartic polynomial is included to most closely match the conditional
expectation that appeared to have four distinct sloped areas.
Findings
CRP acres appear to have a very small effect on HPI. The most basic
first regression shows a negative relationship, while regressions 2
through 4 show a positive relationship. The two models with fixed
effects, regressions 2 and 4, explain much more of the variation in the
data set than the regressions without fixed effects, models 1 and 3.
R-squared values jump from about 0.002-0.006 to 0.904-0.905. Adding the
quartic polynomials do not affect R-squared as much as I expected, with
only a 0.001 difference between regressions 2 and 4. Finally, all
calculated coefficients of interest are statistically significant at the
0.001 level.
Limitations
There are some limitations to these findings.
This is a very good sample of both CRP acres and HPI in the U.S. from
1986-2022. However, a small number of counties never reported CRP acre
values during the entire span of the data. This analysis is limited to
the counties that were able to report CRP values during 1986-2022.
Additionally, these estimates should not be considered causal due to
limitations from omitted variable bias. Many other factors go into the
decision for landowners to put acres into the Conservation Reserve
Program and/or choose to not renew them that also affect housing
prices.
For example, as the economy declines, typically consumers have less
leeway with their finances, and may be less likely to put land into
conservation reserve programs. Housing prices naturally go down during
economic decline as well.
Population growth in certain areas can also affect both variables. If
an area suddenly experiences a population boom, land owners could be
incentivized to sell their extra land to developers rather than put it
into conservation. Housing prices would increase due to population
growth.
Finally, environmental changes like natural disasters could
contribute to omitted variable bias. If natural disasters increase,
there could be an effect on landowners wanting to put additional land
into conservation. The change in conservation acres could be different
between areas that experienced or are more likely to experience the
natural disasters versus areas that are further away. Housing prices may
also change depending on location and proximity to natural
disasters.
Including two way county and year fixed effects helps mitigate some
omitted variable bias, but not all. There could be trends that vary over
time within counties that are not captured by fixed effects.